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# Section 8.3: Exploring the Addition of Complex Waves

Please wait for the animation to completely load.

In this Exploration we investigate how two and three time-dependent plane waves can be added together to begin to resemble a localized wave packet (in Section 8.4 you can add up to 40 plane waves together). **In the animation, ħ = 2m = 1.** Restart.

- With the default settings, explain why the arguments of the cosines and sines are of the form (5*x-25*t) and (-5*x-25*t). In other words, what does the ±5 signify and what does the 25 signify? Remember that
*ħ*= 2*m*= 1 in this animation. - With the default settings, describe the sum of the two plane waves. Look at the real and imaginary parts of the wave functions to verify your conjecture.
- Now change wave functions 2 and 3 to re2 = 1*cos(4*x-16*t), im2 = 1*sin(4*x-16*t), re3 = 1*cos(6*x-36*t), and im3 = 1*sin(6*x-36*t). What results? Now change the number multiplying plane wave 2 and plane wave 3 to 0.5. What wave results now? How does this superposition accomplish this result?

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